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We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient flow calibration in the sense of the recent work of Fischer et al. (2020) for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions. [ABSTRACT FROM AUTHOR]

• The CA relaxation profile was used to determine the advancing CA of sessile drop. • Sessile drop of surfactant solution was formed from an equilibrated pendant drop. • Two advancing contact angles were detected for TX-100 and C 12 E 6 solution drops. • Only one advancing CA was detected for the sessile drop of SDS solution. • Pre-equilibration of the drop before deposition affected the CA relaxation profile. This study investigated the uniqueness of advancing contact angle (CA) by examining the evaporation process of a sessile drop of surfactant solution [sodium dodecyl sulfate (SDS), hexaethylene glycol monododecyl ether (C 12 E 6) and Triton X-100 (TX-100)] on parafilm. The sessile drop was formed from a pendant drop that had reached its equilibrium surface tension in an atmosphere with ∼100% humidity. The relaxation of the drop profile and wetting diameter were recorded from the moment the drop touched the parafilm, and the data were then analyzed to determine the advancing CA. The results showed that for SDS solution drops, only one advancing CA was observed at each SDS concentration. However, the experimental data of TX-100 and C 12 E 6 solution drops indicated the presence of two distinct regions that showed a near-constant CA with a quasi-equilibrium advance of the triple line; hence matching the definition of an advancing CA. The possibility of the existence of two advancing CA was further explored and the presence of two advancing CA for the sessile drops of TX-100 and C 12 E 6 solution was verified by closely examining the advance of the triple line. [ABSTRACT FROM AUTHOR]

This paper reviews the current status of boiling heat transfer modelling, discusses the need for its improvement due to unresolved intriguing experimental findings and emergence of novel technical applications and outlines the directions for an advanced modelling approach. The state-of-the-art of computational boiling heat transfer studies is given for: macro-scale boiling models applied in two-fluid liquid-vapour interpenetrating media approach, micro-, meso-scale boiling computations by interface capturing methods, and nano-scale boiling simulations by molecular dynamics tools. Advantages, limitations and shortcomings of each approach, which originate from its grounding formulations, are discussed and illustrated on results obtained by the boiling model developed in our research group. Based on these issues, we stress the importance of adaptation of a multi-scale approach for development of an advanced boiling predictive methodology. A general road-map is outlined for achieving this challenging goal, which should include: improvement of existing methods for computation of boiling on different scales and development of conceptually new algorithms for linking of individual scale methods. As dramatically different time steps of integration for different boiling scales hinder the application of full multi-scale methodology on boiling problems of practical significance, we emphasise the importance of development of another algorithm for the determination of sub-domains within a macro-scale boiling region, which are relevant for conductance of small-scale simulations. [ABSTRACT FROM AUTHOR]

Abstract The nucleation and lateral growth are more and more important steps for the thin film growth of a phase (silicide, intermetallic…) when the thin film thickness is in the range or below 10 nm. It might become crucial for contact in microelectronics that are in this range of thickness for actual devices and affect the properties of contacts in different parts of the devices. For reaction between 10 nm Ni(10%Pt) and (100)Si, it was shown that NiSi grows by nucleation and lateral growth at the epitaxial θ-Ni 2 Si/Si interface and forms precipitates having a large aspect ratio (large diameter and small thickness) were observed. In this work, the precipitate shape as well as the shape of the different interfaces close to the triple line are reproduced by using the model of Pasichnyy and Gusak for θ-Ni 2 Si/Si interfaces that are either curved or straight. The deduced interfacial energies and kinetics parameters enabling to obtain the characteristics of the precipitates are discussed and compared to the ones obtained by the model of El Kousseifi et al. The conditions for mechanical equilibrium and the implication for the contact formation are discussed. Graphical abstract Unlabelled Image Highlights • NiSi precipitates at the θ-Ni 2 Si/Si interface by nucleation and lateral growth are observed by TEM • The shape of the precipitates is compared to two models of lateral growth • The model of Pasicchnyy and Gusak fits the interfaces shape close to the triple line. • Parameters governing lateral growth (energies, kinetics …) are determined. • Implications of lateral growth on contacts in microelectronics are discussed. [ABSTRACT FROM AUTHOR]

The evaporation process of the thin film region near the triple line for a liquid suspended with nanoparticles involves important interfacial phenomena such as contact line movement, deposition, and evaporation. In this paper, droplets that are seeded with fluorescent nanoparticles of different diameters and of the same particle numbers were investigated for their evaporation rates, deposition patterns, and in-plane average velocities within the field-of-view. The results present different modes of deposition patterns for the fluorescent nanoparticles, and stronger evaporation can be obtained using nanoparticles of small diameter. The temporal and spatial evolution of velocities and thicknesses in the thin films near the triple lines during the droplet evaporation were obtained by using a proposed sub-region method, which is developed from an evanescent wave based nanoparticle image velocimetry technique. It shows that, depending on the nanoparticle size, the spatial variation of the local thin film thickness can be linear or nonlinear. The fluorescent nanoparticles can affect the evaporation modes, the internal flow, and the temporal and spatial evolution of the thin film during the droplet evaporation through the interaction between the particles and the interface near the contact line and their influence on the change of the microscopic contact angle during the pinning process of the contact line. This work can help capture insights on how nanosized particles affect the droplet evaporation near the triple line. [ABSTRACT FROM AUTHOR]

An analytical model for heterogeneous bubble growth during nucleate boiling with variable wettability on an ideal smooth surface has been developed. We analyzed the growth of bubbles in terms of the motion of the triple line, and three stages of bubble growth were identified based on the triple line motion. The transition points between these stages were modelled using a free-energy analysis and force-balance of the bubble growth system. We considered two bubble-growth pathways: one with a constant angle between the liquid–vapor interface and the surface, and one with a constant base (i.e., constant triple line), and the two paths are linked during a bubble growth. It is hypothesized that the transition from a regime to another is linked to the less expansive energy path. To confirm this, a bubble growth was experimentally observed on various different wettability surfaces, and the results of these experiments were compared with the analytical model. In general, a larger contact angle (i.e., a more hydrophobic surface) resulted in bubble growth with a larger triple line, and hence a larger base diameter and a larger departing bubble diameter. [ABSTRACT FROM AUTHOR]

Contact line dynamics occurs in wetting and dewetting phenomena. The dynamics of the triple line (line of contact of the gas, liquid, and solid phases) is considered for a Bingham fluid. The previous analysis of de Gennes for Newtonian fluids is extended, considering the moving liquid near the triple line as having a perfect wedge border. The velocity profile near the contact line is obtained along with the size of the plug flow region. The viscous dissipation is found by limiting the liquid thickness to a lower limit of molecular size. The relation between the triple line velocity and the dynamic contact angle is obtained; the result requires trial and error calculations, and is shown to yield de Gennes’ equation as the Bingham fluid yield stress tends to zero. The requirement for the ideal wedge approximation is considered. [ABSTRACT FROM AUTHOR]

The dynamic behavior of water drops evaporating from poly(methyl methacrylate) (PMMA) substrates with different roughness was examined. The relaxation of the wetting diameter, height, volume and the contact angle of a drop was monitored during the evaporation process. For the smoother substrates with R q ≤ 19 nm, four stages were identified during evaporation: the initial spreading stage, the constant contact radius (CCR) stage, the constant contact angle (CCA) stage, and the final stage. In contrast, for substrates with large roughness ( R q ≥ 209 nm), the CCA stage was not observed, and the contact line was pinned at its original position during almost the entire lifetime of the drop. The energy barrier associated with the pinning and depinning of the contact line was estimated using the Shanahan model, and the energy associated with PMMA substrates of roughness R q = 4.9 and 19 nm was found to be on the order of 10 − 8 J/m. The influences of the liquid withdrawal rate and the internal flow field were also studied, and the weak to strong pinning transition was found to be roughness dominant. [ABSTRACT FROM AUTHOR]

The dynamics of triple line and bubble growth were investigated inside water, gold, silver, and alumina nanofluids. The presence of nanoparticles was found to modify the behaviour of the triple line, depending on nanoparticle materials. Two analytical expressions were developed, one for the contact angle of bubbles and another for the contact angle of droplets, using force balance in the horizontal direction. It was mathematically proven that these analytical expressions are the exact analytical solutions of the Young-Laplace equation. These analytical expressions prove that the Young equation cannot be an accurate force balance at the triple line for axisymmetric bubbles and droplets. The analytical expressions predict the contact angle of bubbles and droplets and prove theoretically that the contact angles of axisymmetric bubbles and droplets depend on volume or size, which agreed with existing experimental data. The predictions of the analytical expressions were compared with experimental data, and close agreements were observed. To reduce uncertainty and error, these two analytical expressions can be used instead of the Young equation, particularly in CFD calculations, to predict the behaviour of triple line or fluid flow in the vicinity of substrate for droplets and bubbles. [ABSTRACT FROM AUTHOR]